Global mean estimation using a self-organizing dual-zoning method for preferential sampling

Giving an appropriate weight to each sampling point is essential to global mean estimation. The objective of this paper was to develop a global mean estimation method with preferential samples. The procedure for this estimation method was to first zone the study area based on self-organizing dual-zoning method and then to estimate the mean according to stratified sampling method. In this method, spreading of points in both feature and geographical space is considered. The method is tested in a case study on the metal Mn concentrations in Jilin provinces of China. Six sample patterns are selected to estimate the global mean and compared with the global mean calculated by direct arithmetic mean method, polygon method, and cell method. The results show that the proposed method produces more accurate and stable mean estimates under different feature deviation index (FDI) values and sample sizes. The relative errors of the global mean calculated by the proposed method are from 0.14 to 1.47 % and they are the largest (4.83–8.84 %) by direct arithmetic mean method. At the same time, the mean results calculated by the other three methods are sensitive to the FDI values and sample sizes.